Geodesic
Determinant representation of Pade joint approximations
Problemy fiziki, matematiki i tehniki, no. 4 (2010), pp. 46-49

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Determinant formulas for numerators and denominators of joint approximations of Pade $\pi_j(z), j=1,2 \dots,r$ of perfect system of functions $\{f_j(z)\}^r_{j=1}$ are established. The analogue of the Pade theorem is proved and the obvious kind of the remainders is found at the approach $f_j(z)$ by the rational function $\pi_j(z)$ . The received theorems supplement and generalise the known results of Ermite, Pade, K. Mahler, E.M. Nikishin, A.I. Aptekarev and other authors.
Keywords: sedate a number, approximations of Pade, joint approximations of Pade, perfect system of functions, determinant representation. 
@article{PFMT_2010_4_a7,
     author = {A. P. Starovoitov and N. V. Rjabchenko},
     title = {Determinant representation of {Pade} joint approximations},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {46--49},
     publisher = {mathdoc},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2010_4_a7/}
}
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A. P. Starovoitov; N. V. Rjabchenko. Determinant representation of Pade joint approximations. Problemy fiziki, matematiki i tehniki, no. 4 (2010), pp. 46-49. http://geodesic.mathdoc.fr/item/PFMT_2010_4_a7/